and
theory (physics), model (physics)
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
Where a system of quantum mechanics is specified by
a Hilbert space ;
a hermitean operator on – the Hamiltonian;
a system of supersymmetric quantum mechanics has
an odd operator in , the supercharge
such that is the Hamiltonian.
If we regard the Hamiltonian as the generator of the Poincare Lie algebra in one dimension, then the graded commutator is the supersymmetry extension to the super Poincare Lie algebra.
The data of a system of supersymmetric quantum mechanics may also be formalized in terms of a spectral triple.